Parametric Intrusive Reduced Order Models enhanced with Machine Learning Correction Terms

TL;DR

This paper introduces a parametric reduced order modeling approach enhanced with machine learning correction terms, improving accuracy in turbulent flow simulations by reintroducing neglected effects.

Contribution

It extends existing ROMs by integrating machine learning to adaptively reintroduce turbulence and mode contributions across parameters.

Findings

Enhanced pressure and velocity accuracy in test cases

Effective use of neural networks for correction terms

Improved ROM performance over standard models

Abstract

In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in standard ROMs are not taken into account. In particular, in this work we consider two types of contributions: the turbulence modeling, added through a reduced-order approximation of the eddy viscosity field, and the correction model, aimed to re-introduce the contribution of the discarded modes. Both approaches have been investigated in previous works and the goal of this paper is to extend the model to a parametric setting making use of ad-hoc machine learning procedures. More in detail, we investigate different neural networks' architectures, from simple dense feed-forward to Long-Short Term Memory neural networks, in order to find the most suitable model for the re-introduced contributions. We tested the methods on two test cases with different behaviors: the periodic turbulent flow past a circular cylinder and the unsteady turbulent flow in a channel-driven cavity. In both cases, the parameter considered is the Reynolds number and the machine learning-enhanced ROM considerably improved the pressure and velocity accuracy with respect to the standard ROM.